# The Great Stellated Dodecahedron

A non-convex polyhedron bounded by twelve intersecting pentagrams; three meeting at each vertex.

The great stellated dodecahedron is one of the four Kepler-Poinsot Star Polyhedra, and is also the third and final stellation of the dodecahedron.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges No. ofFaces SymmetryGroup Dual Polyhedron (5/2)3 3 | 2 5/2 20 30 12 A5×C2 Great Icosahedron

Edge ratios:

• e/r = sqrt(50+22sqrt(5))
• e/rho = 3 + sqrt(5)
• e/R = (1+sqrt(5))/sqrt(3)
• e/e_(12) = (11+5sqrt(5))/2

where e is the edge length, r is the in-radius, rho is the inter-radius, R is the circum-radius, and e_(12) is the edge of the inner dodecahedron.